DTIC ADA461610: Distributed Assignment of Codes for Multihop Packet-Radio Networks

6 Pages·0.08 MB·English

by  Defense Technical Information Center

DISTRIBUTED ASSIGNMENTOFCODES FORMULTIHOPPACKET-RADIONETWORKS
J.J.Garcia-Luna-Aceves andJyotiRaju
ComputerEngineeringDepartment
School ofEngineering
UniversityofCalifornia
Santa Cruz,CA95064
jj,[email protected]
Abstract—Thispaperdescribesandanalyzesadistributedalgorithmfor discussedbyChlamtacandKutten[4]; thedistributedversionof
assigning codes ina dynamic, multihop wireless radio network. The algo- theprotocolusesatravellingtoken,whichincursmoreoverhead
rithm does notrequire any form of synchronization andis completely dis-
traffic on the network. Chlamtac and Kutten also show that de-
tributed. Thealgorithm canbeusedforboththetransmitter orientedand
receiverorientedcodeassignment.Thealgorithmisproventobecorrectand signing a protocol such that the least amount of channel band-
itscomplexityisanalyzed. Theimplementationofthecodeassignmentalgo- widthisusedforbroadcastisNP-complete. Adifferentapproach
rithmaspartofthemediumaccesscontrol(MAC)androutingprotocolsofa tothetoken-basedschemeconsistsofusingcontrolsegmentsdur-
multihoppacket-radionetworkisdiscussed.
ing which the schedulefor the transmission segmentsis decided
[5]. The transmitter-oriented code assignment is introduced in
I. INTRODUCTION [11].Here,quasiorthogonalcodesareassignedtotransmittersina
Using code division multiple access (CDMA) in packet-radio packet-radionetworkinsuchawaythathiddenterminalinterfer-
networks permits multiple stations within range of the same re- enceiseliminated. Therearemanyapproachesbasedonthefact
ceivers to transmit concurrently, without interference. Several that the node needs to know the information of nodes two-hops
multiaccess protocols have been proposed and commercial sys- away[6],[3],[9].
temshavebeendeployedthattakeadvantageof CDMA [1]. An This paper presents a distributed code assignment algorithm.
important design consideration in a multihop packet-radio net- This algorithm assigns a code to each node in a way that no in-
work using CDMA is the assignment of transmission codes to terferenceoccursafterthealgorithmconverges,providedthatthe
network nodes. In a large network, the number of transmission numberofcodesavailableforassignmentisatleast ,
codes is smaller than the number of nodes, and senders and re- where isthemaximumnumberofone-hopneighbdo(rds(cid:0)an1y)n+od2e
ceivers must agree on which transmission code to use in a way can havde. This is because the algorithm assigns a transmission
thatavoidsinterferenceasmuchaspossible. code to a nodethat is differentthan the codesassigned to nodes
Interference in a CDMA network can be of two kinds. Di- two hops away from the node. The algorithm is designed to be
rect interference consists of two neighboring nodes transmitting partoftheMACandroutingprotocolsofamultihoppacket-radio
to each other at the same time. This can be avoided by using a network.Itisbasedontheasynchronousexchangeofcontrolmes-
randomaccessprotocolthatschedulestransmissionstotheneigh- sagesthatarepartoftheregularMACandroutingmessages,and
bornodesintimetoavoidcollisions(e.g.,FAMA[8]). Secondary theinformationgeneratedbyanyonenodepropagatesuptotwo
interference consists of two senders transmitting to receivers in hopsawayfromthenode.
away thatthe senders’ transmissionsinterfereatat leastonere-
ceiver. Thistypeofinterferencecanoccurin two scenarios.Two A 1
stationsunawareofeachother’sexistencecantransmittothesame
receiveratthesametime;thisgivesrisetothetransmitter-oriented
2 1
codeassignmentproblemshowninFig.1. Here, and ,which C
aretwohopsawayfromeachotherneedtohaveAdiffereCntcodes. B
Thesecondcaseofsecondaryinterferenceoccurswhenastation Fig.1. Interferencewhentwotransmitterstwo-hopsawayhavethesamecode
is transmitting to its neighbor and a third station’s transmission
to somestation otherthanthe stationsinvolvedin thefirsttrans-
mission causes an interference with the first transmission. This C
leadstothereceiver-orientedcodeassignmentproblemillustrated
1 D
inFig.2. Here, istransmittingto butcausesinterferenceat
, because anCd which are twoDhops away share the same 1
cBode. AscanBbeseeDnfromtheearliertwoexamples,thecodeas- A B
signment problem requires that no set of stations which are two
Fig.2. Interferencewhentworeceiverstwo-hopsawayhavethesamecode
hopsawayhavethesamecode.
Several approaches have been proposed in the past for chan-
Section II describesthealgorithmin detail. Section III shows
nel/code assignments. A tree-based protocolfor broadcasting is
thatthealgorithmguaranteescorrectcodeassignmentsaftercon-
vergence, provided that enough codes are available. Section IV
ThisworkwassupportedinpartbytheDefenseAdvancedResearch Projects
Agency(DARPA)undergrantDAAB07-95-C-D157. addressesthealgorithm’scomplexity.
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1. REPORT DATE 3. DATES COVERED
1997 2. REPORT TYPE 00-00-1997 to 00-00-1997
4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
Distributed Assignment of Codes for Multihop Packet-Radio Networks
5b. GRANT NUMBER
5c. PROGRAM ELEMENT NUMBER
6. AUTHOR(S) 5d. PROJECT NUMBER
5e. TASK NUMBER
5f. WORK UNIT NUMBER
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION
University of California at Santa Cruz,Department of Computer REPORT NUMBER
Engineering,Santa Cruz,CA,95064
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11. SPONSOR/MONITOR’S REPORT
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13. SUPPLEMENTARY NOTES
14. ABSTRACT
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a. REPORT b. ABSTRACT c. THIS PAGE 5
unclassified unclassified unclassified
Standard Form 298 (Rev. 8-98)
Prescribed by ANSI Std Z39-18
II. THEALGORITHM C. InformationatEachNode
A. NetworkModelandProtocolAssumptions Thefollowingstructuresareneededforcodeassignmentateach
node.
To describe our code assignment algorithm, we model a mul-
Priority List: Each node has a unique priority number as-
tihop packet-radio network as an undirected graph
(cid:15)
where isthesetofnodesand isthesetofedgesG. E=ach(Vn;oEde) signedtoit. Thisprioritynumberallowstwo-hopneighbors
consistVsofatransceiverandaroEuter. Alinkbetweentwonodes withthesamecodetodecidewhichoneofthemshouldkeep
and in meansthat canhear ’stransmissionand canheair the code and which must look for new codes. We decided
’s trjansmGission. Eachinodeusesjan omnidirectionalajntennafor to use the addressof a nodeas its prioritynumber,because
itransmissionand the networkworksin half-duplexmode, which addressesareunique.
Theprioritylistcontainstheprioritynumbersofthenode,its
meansthat a nodecannottransmit and receiveat the same time.
one-hop and two-hop neighbors sorted in increasing order.
Aroutingprotocolisassumedtocreateandupdatetheroutingta-
Eachentryinthelisthasaflagwhichissetto1iftheneigh-
bleusedateachnode.Thisroutingprotocolprovidesinformation
bor is one-hop or 2 if the neighbor is two-hop. The codes
aboutwhothenode’sactiveneighborsare;thisinvolvesaddingto
assignedtothenodeanditsneighborsarealsolistedinhere.
theneighborlistnewneighborswhentheycomeupanddeleting
Neighbor List : This is a list of all the node’s immediate
neighborswhicharenolongeractive. Theroutingprotocolisas-
(cid:15)
neighbors,i.e. allitsone-hopneighbors.
sumedtohavesomeformofneighbordiscoverymechanismsuch
Code Assignment Message Retransmission List (CAMRL):
asaHELLOexchange[12].Nodesprocessmessagestheyreceive
(cid:15)
This list has one or more retransmission entries, where an
andlinkstransmitpacketsintheFIFOorder.
entryisofthefollowingnature.
WealsoassumeaMACprotocolthatallowsstationstosched-
– ThesequencenumberoftheCAM.
uletheirtransmissionstothesamereceiverinawaythatcollisions
– Aretransmissioncounterthatisdecrementedeverytimethe
ofdatapacketstothereceiversareavoided. Theflooracquisition
nodesendsaCAM.
multipleaccess(FAMA)familyofprotocols[8]isanexampleof
– An ACK-requiredflag thatis actuallya field of thesize of
such a MAC protocol. According to FAMA, a sender transmits
the neighborlist. The bit correspondingto a neighbor is
a request-to-send (RTS) to the receiver, which in turn transmits
setiftheCAMisyettobeacknowledgedbytheneighbor.
a clear-to-send (CTS) if it obtains the RTS free of errors. The
TheCAMRLpermitsanodetoknowwhichCAMisnotac-
RTSlastslongerthanthepropagationdelayandtheCTSmustbe
knowledgedby some of theneighborsand needs to besent
larger than size of RTS + maximum round trip propagation de-
again. The node retransmits a CAM when its retransmis-
lay + transmit-to-receiveturnaround time, so that collisions due
sion entry in the CAMRL reaches zero. The retransmission
tohiddenterminalsareeliminatedintheabsenceoferasuresdue
counterofanewentryintheCAMRLissetequaltoasmall
to drastic node mobility. When the network is first brought up,
number(e.g.,3or4).
alltransmissionstakeplaceoveracommonsignalingcodeusing
UnassignedCodeList(UCL):Thislistcontainsallthecodes
FAMA.Asthestationsdecideontheircodes,thestationsusedif-
(cid:15)
whichareavailable,i.e.theyarenotbeingusedbyanyofthe
ferentcodesfordatatransmissions.
node’stwo-hopneighbors.
A link is assumed to exist between two nodes only if there is
good radio connectivity and the update messages of the routing
D. InformationExchangedamongNodes
protocol can be sent reliably. Node failures are modelled as all
links incident on the node failing at the same time. A moving TheCAM’spropagateonlyfromanodetoitsneighborsandno
nodeisconsideredattachedtoallnodeswithwhichthenodecan further.EachCAMcontains
exchangemessageswithacertainprobabilityofsuccess;amoving TheaddressofthenodewhichissendingtheCAMalongwith
(cid:15)
nodebecomesdetachedfromnodeswithwhichitcannotexchange itscode.
messages with this probability of success. The codeassignment The addresses of the node’s one-hop neighbors along with
(cid:15)
algorithmrunsinconjunctionwiththeroutingprotocol,whichin theircodes.
turnrunsontopoftheMACprotocol. ACK’sto earlierCAM’s. AnACKentryspecifiesthesource
(cid:15)
andthesequencenumberoftheCAMbeingacknowledged.
B. PrinciplesofOperation
Aresponselistofzeroormorenodeswhichneedtosendan
(cid:15)
The messages of the code-assignment protocol are called the ACKforthisCAM.
Code Assignment Messages (CAM). These messages are sent as IfasingleCAMisnotlargeenoughtoholdallthecodesand
partofthemessagesexchangedinthenetwork’sroutingprotocol. addresses,theinformationcanbesplitupintomorethanone
These messages could be lost due to changes in radio connec- CAM.
tivity. Reliable transmissions of CAM’s is donewith the help of CAM’saresentinthefollowingsituations.
retransmissions. After receivinga CAM, the receiveris required 1. A new node comes up. Its priority list only consists of its
to acknowledge it to the node which sent it, by sending an ex- own address and its own code. It broadcasts this to all its
plicit ACK message indicating that the CAM has been received neighbors.
andprocessed. Since,thenetworklayerassumesthelinktobeof 2. When a node detectsa changeof codeby any of its one-
a broadcastnature, a node can send a messageonceand assume hop neighbors,i makes the required changes in its priority
tohavesentittoalltheneighbors;however,eachneighborneeds list andsendsaiCAM to allitsone-hopneighborsincluding
toACKthemessageindividually. theonethatchangedthecode.
2
3. Whenanode findsthatacertainone-hopneighbor isno G. ProcessinganACK
longeractive,iitdrops fromtheprioritylist. Thisinfjorma-
The ACK entry bears the sequence number of the CAM it ac-
tionisthenconveyedtjoallitsone-hopneighborsbyaCAM
knowledges. AssoonasanACKisreceivedbyanode,thenode
whichreflectsthechanges.
searchesitsCAMRLtofindtheentrywiththerequiredsequence
E. UpdatingthePriorityList number.IfamatchisfoundthenoderesetstheACKrequiredflag
fortheneighborwhichsenttheACK.
A nodeupdates its priority list either after detecting a change
AnodemayreceiveanACKforanentrywhichhasbeendeleted
ofcodeinoneofitsone-hopneighborsorafterreceivingaCAM
due to more recent CAM’s to the same neighbor or for an entry
whichcontainsinformationaboutachangeofcodebyitstwo-hop
which has undergonea changein sequencenumberdue to more
neighbors.
recentretransmissions. Inthatcase, the nodesimply ignoresthe
When a node notices a change of code in any of its one-hop
ACK.
neighbors, it makes a change in its own priority list and sends
a CAM with its own address and the address of all its one-hop H. EmbeddingCodeAssignmentAlgorithminMACandRouting
neighbors along with their respective codes. This is sent to all Protocols
itsone-hopneighbors. Ifatwo-hopneighborhaschangedacode
Theproposedcodeassignmentalgorithmcanbeusedasanin-
thenanyofthefollowingthreesituationsmightarise.
tegralpartoftheMACandroutingprotocolofapacket-radionet-
1. Ifthenewcodeofthetwo-hopneighborisnotthesameas
work.
’scode,thenthenewcodeinenteredintotheprioritylistin
itheentrycorrespondingtothetwo-hopneighbor. In our model, all stations have a common signaling code on
whichtheyimplementanRTS-CTSexchangesimilartothe802.11
2. If the new codeof the two-hop neighboris the same as ’s
codeandtheaddressof thetwo-hopneighboris lesser thian protocol[10].Thedatatransfercanbedoneonthereceiver’scode
forROCAoronthetransmitter’scodeforTOCA.Theadvantageof
’scode, then picksupanewcode. The newcodesof the
itwo-hopneighiborand areenteredintotheprioritylist. someformofcodeassignmentisthatanode’sone-hopneighbor
3. If the new codeof theitwo-hop neighboris the same as ’s canreceiveadatatransmissionatthesametimeasthenode.
codeandtheaddressofthetwo-hopneighborisgreaterthian
’scode,then retainsitscodeandthereisatemporarycon- RTS
fliicttillthetwoi-hopneighborchangesitscode.Thetwo-hop I Sender(Signalling Code)
neighbor will get to know of ’s code because of the CAM
sentbytheone-hopneighboroif .Thisconflictdoesnotstop CTS
the data transfer in the networki. It merely increases colli- J Receiver(Signalling Code)
sions.
Data Train 1 Data Train 2
In the first two cases the UCL has to be updated. All the codes DATA DATA
1 2
used by the two-hop neighborsare marked as unavailable in the
I Sender(Receiver’s Data Code) Interval Time
UCL.
Fig.3. HandshakeandDataTransferusingReceiver’sCode
F. SendingNewandRetransmittedCAM’s
Wheneveranode sendsanewCAM,itmustdothefollowing Weinvestigatethecaseforthereceiverorientedapproach(Fig.
steps i 3). Considertwo nodes and which areimmediateneighbors
1. Decrementtheretransmissioncounterofallthenewentries of each other. The nodeI neeJds to transmit data to . sends
intheCAMRL. anRTSto inwhichitspIecifiesthecodeitexpects JtohIave. It
2. Delete the entries which correspond to entries in the new alsospecifiJesthenumberofdatapacketsitplanstosJend. send
CAM. backaCTSwhichcontainsitscodeandthemaximumnumJberof
3. AddanentryintheCAMRLforthenewCAM. data packets it can allow. After successfully receiving the CTS,
If a certain CAM in the CAMRL has all its entries covered be a thenode transmitsitsdatausingthecode.
newCAMtransmission,theoldCAMisdeletedfromtheCAMRL. AfterthIespecifiednumberofdatapacketshavebeentransmit-
WhentheretransmissioncounterforaCAMretransmissionen- tedandreceived, and switchbacktothesignalingcode.Ifthe
try expires, node sends a new CAM which has the same data RTS-CTS exchangIe alsoJspecifies the interval time between two
as the old CAM. Hiowever, it has a new sequence number and a packetbursts, thenafteran initialhandshake canswitch to ’s
newresponselist. Thisnewresponselistspecifiestheneighbors data code automatically without an interveniIng RTS-CTS hanJd-
whichdidnotacknowledgetheCAMearlier. Theoldentryinthe shake. The last packet of a data burst can contain control data
CAMRLisdeletedandanewentrycreatedforthenewretransmis- which specifies if there are more data bursts following. If node
sion. gets any requests which would require it to receive data from
Usingtheaboveretransmissionstrategy,anodecankeepsend- Janynodeotherthan duringthetimeithasreservedfor ,itwill
ingCAM’stillallitsone-hopneighborsacknowledgeit. However, refusetherequests.AIlso,anyRTSarriving(onthesignalinIgcode)
aftersometimeifanodegetsnoresponsefromaneighbor,itcon- at whileitisreceivingdatafrom (on ’sdatacode)wouldnot
siderstheneighbordeadanddoesnotsenditanyCAM’sandresets deJstroythedata.ThistakescareofIthemJultihopproblem.
bitswhichcorrespondtothisneighborintheresponselistsofall Now,withtheavailabilityofassuredtimefordatatransmission,
theentriesinthe . acertainratefordatatransmissioncanbeguaranteed.Thisisuse-
CAMRL
3
fulforreal-timedatatrafficwhichrequiresconstantdelay. How- hopandtwo-hopneighbors. Thisallowsthemtocalculateacode
ever,onehastokeepinmindthatifthetopologygetsconstantly forthemselveswhichisdifferentfromthecodesofalltheirtwo-
rearranged,sucharatecannotbesustained. hopneighbors.
Asimilartreatmentcanbedoneforthetransmitterorientedap- Definition1: Therearetwodifferentwaysanodecanchange
proach.Here,theRTS-CTSwillexchangethesender’scode. itscode.
CAM’s need to contain information about a node’s one-hop 1. Thenodecanchangeitscodetoanyoftheunusedtwo-hop
neighborsandtheir codes. If thedistancemetricin aroutingal- codes(thisincludescodesofone-hopneighbors).
gorithmishop-count,thenreadingaroutingupdatemessagefrom 2. Thenodecanchangetoacodethatisalreadybeingusedby
a node is enough for the code assignment algorithm to deduce atwo-hopneighborwithanaddressgreaterthanitself.
anode’sone-hopneighbors. However,thecodesassignedto the
Definition2: Anodeissaid tohaveconsistentinformationin
neighborsarenotpresentintheroutingupdates.Withtheaddition
its priority table if it has the most recent information about the
ofthisfieldtheroutingupdatescanbeusedasCAM’s.
changeofcodesofitsone-hopandtwo-hopneighbors.
Theorem1: Afinitetimeafter ,allnodeshaveconsistentin-
III. CORRECTNESS OFTHEALGORITHM formationintheirprioritytablesat0ndthecodestheydecidebased
Thissectionshowsthatthecode-assignmentprotocoliscorrect onthisinformationarecorrect.
undertheassumptionthatanunderlyingprotocolassuresthefol- Toprovetheabovestatementweneedtoshowthatthefollow-
lowingconditions. ingconditionsaresatisfied:
1. A node detects within a finite time the existence of a new
1. Allnodeseventuallystopupdatingtheirprioritylistandstop
neighbororthelossofconnectivitywithaneighbor.Anode
sendingupdatemessagestotheirneighbors.
alsodetectswithinafinitetimeachangeinthecodeusedby
2. All nodes must have consistent code information in their
aneighbor.
topologydatabaseswithinafiniteamountoftimeafter .
2. Allmessagestransmittedoveraradiolinkarereceivedcor- 3. Iftheinformationinthenodeisconsistentandmostretc0ent,
rectlyandinthepropersequencewithinafinitetime.
a nodeonly makes a valid changeof code and there are no
3. Allmessagesandcodechangesareprocessedoneatatime
deadlocks.
within a finite time and in the order in which they are de-
4. Ifallnodesmakeonlyvalidchangeofcodes,thenwehavea
tected.
correctcodeassignment,suchthatnopairoftwo-hopneigh-
borshavethesamecode.
Lemma1:Allnodeseventuallystopupdatingtheirprioritylist
D-1 andstopsendingupdatemessagestotheirneighbors.
Proof: First,notethatthereareafinitenumberofnodesinthe
D-1
network,andthatbyassumptionafinitenumberofcodechanges
can occur upto time , after which no more changes in codes
D-1
D occur. Alsobyassumpt0tion,achangeofcodebyacertainnodeis
detectedwithinafiniteamountoftimebytheneighboringnodes.
These neighboring nodes, in turn update their priority lists and
D-1
sendoutatmostone toeachoftheirneighbors.Therefore,
Fig.4. Theconnectivityofanodeinanetworkamaximumdegreed forany changeof coCdeA, tMherecanbeat most messages
sent. d(d(cid:0)1)
Another assumption we make is that we have a minimum of Anodewhichdoesnotallowtheprotocoltoterminatemustbe
codes, where is the maximumdegreeof thenet- generating an infinite amount of ’s. This is only possible
dw(odrk(cid:0).O1)ne+c2odeisrequiredfdorsignalingandtheuseoftherestof if oneofits neighborsischangingCiAtsMcodeaninfinitenumberof
themcanbeexplainedusingFig. 4. Anodecanhaveamaximum times. Since,weassumethattherearenochangesafter ,thisis
of neighbors.Eachoftheseneighborscaninturnhave neigh- notpossible. Therefore,theprotocolproducesonlyafinti0tenum-
bords. Considerthecentralnode . Ithas one-hopneighbdorsand berof ’sandthemessagetransfermuststopwithinafinite
two-hopneighbors. Thienodesdhouldnothaveacodein timeafCteAr M.
dco(dm(cid:0)mo1n)withanyofitstwo-hopneighbors. Thus,itisclearthat Lemmat02: Allnodesmusthaveconsistentcodeinformationin
we require codes. This is a sufficientconditionto theirtopologydatabaseswithinafiniteamountoftimeafter .
obtainvaliddc(odd(cid:0)ea1s)si+gn1ments[9]. Thenetworkcanstill operate Proof:Consistentcodeinformationmeansthatthenodeknto0ws
withfewerthan ,eventhoughsometwo-hopneigh- about all the recent code changes in its one-hop and two-hop
borswillhavethed(sdam(cid:0)e1c)o+des2.However,fortheproof,weassume neighbors. Consider some node . A lower level protocolguar-
that codesexist. antees that will detect a changei of code in any of its one-hop
Addd(diti(cid:0)on1a)l+ass2umptions are that there are a finite number of neighborswiithinafinitetime.
codechangesuptotime , andthatnomorechangesoccurafter Consider the case of a node whose two-hop neighbor
that time, and that nodets0can correctly determine which CAM’s changes its code. This two hop nieighbor is the one-hop neighk-
aremorerecentthantheothers. borofoneof ’sone-hopneighbors( ). Weareguaranteedthat
Correctness for this algorithm means that within a finite time detectsachanigein ’scodeinafinitejtime. Thisdetectioncausejs
after ,allnodesobtaininformationaboutthecodesoftheirone- achangein ’spriokritylist,whichinturncauses tosendaCAM
t0 j j
4
toallitsone-hopneighborswhichinclude and . Since,weas- B. ComplexityofComputationattheNodes
sume that node processes ’s in a fiinite tkime, we always
In the worst case there are entries in the . This
havethelatestcojdechangeiCnfAorMmationatanodeinafinitetime includes new entries which diddn+ot1exist in the prioCriAtyMlist ear-
afterthelastchange,i.e. after .
lier. The entries in the are presumed to be in the sorted
t0
Lemma3: Iftheinformationinthenodeisconsistentandmost order. AscanoftheprioCritAyMlistisdoneandthenewcodesadded
recent,anodeonlymakesavalidchangeofcodeandthereareno
to it. While doing the scan we can check if any of the two-hop
deadlocks.
neighborshave the same code and also update the . There
Proof: When a nodegets a CAM, it makeschangesin its pri- are entriesintheprioritylist. AlinUeaCrLscanwill
ority tableandchecksto seeif anyof its two-hopneighborsuse takedt(hde(cid:0)or1d)er+odf +1 whichis .
2
the same code as it does. If no two-hop neighbor has the same d(d(cid:0)1)+d+1 O(d )
code,thenodedoesnothing. Ifatwo-hopneighborhasthesame C. StorageComplexity
code, then thenodechecksthe addressof thetwo-hopneighbor.
Theprioritylisthas entries. The can
Ifthetwo-hopneighborhasalargeraddress,thenthenodekeeps haveaspecified maximdu(md(cid:0)nu1m)b+erdo+f e1ntrieswhich isMprResLumed
itsowncode. Ifthetwo-hopneighborwiththesamecodehasan
tobeaconstant.The hastohaveaminimumof
addresssmallerthanthenode,thenthenodehastopickupanew entries. ThusthestoraUgCeLcomplexityis . d(d(cid:0)1)+2
2
codefromthe . Ifthereare codes,therewillal- O(d )
waysbesomeUcoCdeLavailabletopdic(kd.(cid:0)Th1u)s+,t2hereisalwaysavalid V. CONCLUSIONS
changeofcode.Itcanbeseenthattherearenopossiblesituations
Wehavepresentedanalgorithmfordistributed,dynamicchan-
where a node has to wait for any event to occur and therefore,
nelassignmentinmultihoppacketradionetworks. Thisprotocol
thereexistnodeadlocks.
is based on obtaining information about the transmission codes
Lemma4: Ifallnodesmakeonlyvalidchangesofcodes,then
used by nodes one-hop and two-hops away. The algorithm was
wehaveacorrectcodeassignmentinwhichnotwo-hopneighbors
shown to be correct and its complexitywas analyzed. This pro-
havethesamecode.
tocol fits in nicely with existing MAC and routing protocolsde-
Proof:Considerasetoftwo-hopneighbors sorted
signed for multihop packet-radio networks. At UCSC, we are
with respect to their addresses. Under theac1o;nad2i:t:i:o:n;aonf valid
implementing the proposed algorithm as part of the FAMA [8]
change of codes, no node can have the same code as a two-hop
andWirelessInternetRoutingProtocol[12]whichareusedinthe
neighbor with lesser address, i.e cannot have the same code
WirelessInternetGateways[2],[7].
as , cannothavethesame coad2eas and . If thecondi-
tiona1ofav3alid change of codes is true fora1all nodae2s, any node REFERENCES
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[4] I.ChlamtacandS.Kutten.Tree-BasedBroadcastinginMultihopRadioNet-
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neighbors’codes.Inthiscase,thereareonly messages
2
exchanged. O(d )
2. Thenode’snewcodeisthesameasoneofitstwo-hopneigh-
bors’code. Inthiscase,thetwo-hopneighbormighthaveto
changecodewhichinturncouldcause ’stobesent. In
apathologicalcase,anode’schangeofCcAodMemightcauseall
thenodesinthenetworktochangetheircodes.
From the above, it follows that the number of messages is
boundedby .
2
O(jVj:d )
5